Abstract

Some inputs of computational models are commonly retrieved from external sources (handbooks, articles, dedicated measurements), and therefore are subject to uncertainties. The known experimental dispersion of the inputs can be propagated through the numerical models to produce samples of outputs. The stemming propagation of uncertainties is already significant in metrology but also has applications in optimization and inverse problem resolution of the modeled physical system. Moreover, the information on uncertainties can be used to characterize and compare models, and to deduce behavior laws. This tutorial gives tools and applications of the propagation of experimental uncertainties through models. To illustrate the method and its applications, we propose to investigate the scattering of light by gold nanoparticles, which also enables the comparison of the full Mie theory and the dipole approximation. The position of the localized surface plasmon resonance and the corresponding value of the scattering efficiency are more specifically studied.

© 2017 Optical Society of America

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  1. Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1), “Evaluation of measurement data—Guide to the expression of uncertainty in measurement,” 1st ed., (GUM 1995 with minor corrections) (2008).
  2. Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1), “Evaluation of measurement data—Supplement 1 to the ‘Guide to the expression of uncertainty in measurement’—Propagation of distributions using a Monte Carlo method,” 1st ed., (2008).
  3. Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1), “Evaluation of measurement data—Supplement 2 to the ‘Guide to the expression of uncertainty in measurement’—Extension to any number of output quantities,” 1st ed., (2011).
  4. B. N. Taylor and C. E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results (National Institute of Standards and Technology, 1994) (supersedes NIST Technical Note 1297, January 1993).
  5. L. Kirkup, “A guide to gum,” Eur. J. Phys. 23, 483–487 (2002).
    [Crossref]
  6. D. Barchiesi and T. Grosges, “Inverse problem method: a complementary way for the design and the characterization of nanostructures,” AASCIT Commun. 2, 296–300 (2015).
  7. J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave Version 4.2.0 Manual: A High-Level Interactive Language for Numerical Computations (2016).
  8. A. A. Borovkov, Mathematical Statistics (Gordon and Breach Science, 1998).
  9. H. W. Lilliefors, “On the Kolmogorov-Smirnov test for normality with mean and variance unknown,” J. Am. Stat. Assoc. 62, 399–402 (1967).
    [Crossref]
  10. A. Kolmogoroff, “Sulla determinazione empirica di una legge di distribuzione,” G. Ist. Ital. Attuari 4, 83–91 (1933).
  11. T. W. Anderson and D. A. Darling, “A test of goodness of fit,” J. Am. Stat. Assoc. 49, 765–769 (1954).
    [Crossref]
  12. S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality (complete samples),” Biometrika 52, 591–611 (1965).
    [Crossref]
  13. S. Kotz and N. L. Johnson, eds., Breakthroughs in Statistics: Methodology and Distribution (Springer, 1992).
  14. G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).
  15. S. Kessentini and D. Barchiesi, Nanostructured Biosensors: Influence of Adhesion Layer, Roughness and Size on the LSPR: A Parametric Study (INTECH Open Access, 2013), Chap. 12, pp. 311–330.
  16. H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
    [Crossref]
  17. N. Harris, M. J. Ford, and M. B. Cortie, “Optimization of plasmonic heating by gold nanospheres and nanoshells,” J. Phys. Chem. B 110, 10701–10707 (2006).
    [Crossref]
  18. D. Barchiesi, Numerical Optimization of Plasmonic Biosensors (INTECH Open Access, 2011), Chap. 5, pp. 105–126.
  19. D. H. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1, 67–82 (1997).
    [Crossref]
  20. S. Kessentini, D. Barchiesi, T. Grosges, and M. Lamy de la Chapelle, “Selective and collaborative optimization methods for plasmonics: a comparison,” PIERS Online 7, 291–295 (2011).
  21. S. Kessentini and D. Barchiesi, “Particle swarm optimization with adaptive inertia weight,” Int. J. Mach. Learn. Comput. 5, 368–373 (2015).
    [Crossref]
  22. D. Barchiesi, “Adaptive non-uniform, hyper-elitist evolutionary method for the optimization of plasmonic biosensors,” in CIE 2009 International Conference Computers & Industrial Engineering (2009), pp. 542–547.
  23. T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
    [Crossref]
  24. D. Barchiesi, “Surface Plasmon Resonance Biosensors: Model and Optimization,” in Nanoantenna: Plasmon-Enhanced Spectroscopies for Biotechnological Applications, M. L. De la Chapelle and A. Pucci, eds. (Pan Stanford, 2013), Chap. 11, pp. 333–357.
  25. D. Barchiesi, “Numerical retrieval of thin aluminium layer properties from SPR experimental data,” Opt. Express 20, 9064–9078 (2012).
    [Crossref]
  26. D. Barchiesi, “The Lycurgus cup: inverse problem using photographs for characterization of matter,” J. Opt. Soc. Am. A 32, 1544–1555 (2015).
    [Crossref]
  27. D. Macías, A. Vial, and D. Barchiesi, “Application of evolution strategies for the solution of an inverse problem in near-field optics,” J. Opt. Soc. Am. A 21, 1465–1471 (2004).
    [Crossref]
  28. D. Macias and D. Barchiesi, “Identification of unknown experimental parameters from noisy apertureless scanning near-field optical microscope data with an evolutionary procedure,” Opt. Lett. 30, 2557–2559 (2005).
    [Crossref]
  29. A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation (Society for Industrial and Applied Mathematics, 2005).
  30. J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
    [Crossref]
  31. D. Barchiesi, S. Kessentini, N. Guillot, M. Lamy de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21, 2245–2262 (2013).
    [Crossref]
  32. G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. 33025, 377–445 (1908).
    [Crossref]
  33. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
  34. S. Link and M. A. El-Sayed, “Shape and size dependence of radiative, non-radiative and photothermal properties of gold nanocrystals,” Int. Rev. Phys. Chem. 19, 409–453 (2000).
    [Crossref]
  35. D. Barchiesi and T. Grosges, “Control of the applicability of the dipole approximation for gold nanoparticles,” Adv. Studies Biol. 7, 403–412 (2015).
    [Crossref]
  36. D. Barchiesi and T. Grosges, “Short note on the dipole approximation for electric field enhancement by small metallic nanoparticles,” J. Opt. 17, 114003 (2015).
    [Crossref]
  37. R. Bienert, F. Emmerling, and A. F. Thünemann, “The size distribution of ‘gold standard’ nanoparticles,” Anal. Bioanal. Chem. 395, 1651–1660 (2009).
    [Crossref]
  38. O. P. Na, L. Rodríguez-Fernández, V. Rodríguez-Iglesias, G. Kellermann, A. Crespo-Sosa, J. C. Cheang-Wong, H. G. Silva-Pereyra, J. Arenas-Alatorre, and A. Oliver, “Determination of the size distribution of metallic nanoparticles by optical extinction spectroscopy,” Appl. Opt. 48, 566–572 (2009).
  39. R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
    [Crossref]
  40. W. Haiss, N. T. K. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-VIS spectra,” Anal. Chem. 79, 4215–4221 (2007).
    [Crossref]
  41. Y. Mori, M. Furukawa, T. Hayashi, and K. Nakamura, “Size distribution of gold nanoparticles used by small angle x-ray scattering,” Part. Sci. Technol. 24, 97–103 (2006).
    [Crossref]
  42. H. N. Verma, P. Singh, and R. M. Chavan, “Gold nanoparticle: synthesis and characterization,” Veterinary World 7, 72–77 (2014).
    [Crossref]
  43. P. Stoller, V. Jacobsen, and V. Sandoghdar, “Measurement of the complex dielectric constant of a single gold nanoparticle,” Opt. Lett. 31, 2474–2476 (2006).
    [Crossref]
  44. http://refractiveindex.info , 2016.
  45. L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520, 501–509 (2011).
    [Crossref]
  46. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]
  47. E. D. Palik, Handbook of Optical Constants (Academic, 1985).
  48. R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
    [Crossref]
  49. S. Babar and J. H. Weaver, “Optical constants of Cu, Ag, and Au revisited,” Appl. Opt. 54, 477–481 (2015).
    [Crossref]
  50. K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
    [Crossref]
  51. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
    [Crossref]
  52. A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
    [Crossref]
  53. D. Barchiesi and T. Grosges, “Errata: fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophoton. 8, 089996 (2015).
    [Crossref]
  54. D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
    [Crossref]
  55. D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36, 173–209 (2013).
  56. T. Pagnot, D. Barchiesi, D. van Labeke, and C. Pieralli, “Use of SNOM architecture to study fluorescence and energy transfer near a metal,” Opt. Lett. 22, 120–122 (1997).
    [Crossref]
  57. G. Parent, D. Van Labeke, and D. Barchiesi, “Fluorescence lifetime of a molecule near a corrugated interface: application to near-field microscopy,” J. Opt. Soc. Am. A 16, 896–908 (1999).
    [Crossref]
  58. K. Levenberg, “A method for the solution of certain problems in least squares,” Quart. Appl. Math. 2, 164–168 (1944).
    [Crossref]
  59. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
    [Crossref]
  60. M. Futamata, “Surface-plasmon-polariton-enhanced Raman scattering from self-assembled monolayers of p-nitrothiophenol and p-aminothiophenol on silver,” J. Phys. Chem. 99, 11901–11908 (1995).
    [Crossref]
  61. N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
    [Crossref]
  62. N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
    [Crossref]
  63. J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
    [Crossref]
  64. L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
    [Crossref]
  65. G. Sun, J. B. Khurgin, and D. P. Tsai, “Comparative analysis of photoluminescence and Raman enhancement by metal nanoparticles,” Opt. Lett. 37, 1583–1585 (2012).
    [Crossref]
  66. H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
    [Crossref]
  67. P. J. McNumy, S. D. Druger, M. Kerker, and H. Chew, “Fluorescent scattering by anisotropic molecules embedded in small particles,” Appl. Opt. 18, 1484–1488 (1979).
    [Crossref]
  68. T. Hayakawa, S. T. Selvan, and M. Nogami, “Field enhancement effect of small Ag particles on the fluorescence from Eu3+-doped SiO2 glass,” Appl. Phys. Lett. 74, 1513–1515 (1999).
    [Crossref]
  69. T. Pagnot, D. Barchiesi, and G. Tribillon, “Energy transfer from fluorescent thin films to metals in near-field optical microscopy: comparison between time-resolved and intensity measurements,” Appl. Phys. Lett. 75, 4207–4209 (1999).
    [Crossref]
  70. G. Parent, D. Van Labeke, and D. Barchiesi, “Surface imaging in near-field optical microscopy by using the fluorescence decay rate: a theoretical study,” J. Microsc. 194, 281–290 (1999).
    [Crossref]
  71. C. Baffou, M. Kreuzer, F. Kulzer, and R. Quidant, “Temperature mapping near plasmonic nansotructures using fluorescence polarization anistropy,” Opt. Express 17, 3291–3298 (2009).
    [Crossref]
  72. V. V. Datsyuk and O. M. Tovkach, “Optical properties of a metal nanosphere with spatially dispersive permittivity,” J. Opt. Soc. Am. B 28, 1224–1230 (2011).
    [Crossref]
  73. D. Barchiesi, “Handling uncertainties of models inputs in inverse problem: the U-discrete PSO approach,” in International Conference on Control, Decision and Information Technologies (CoDIT), I. Kacem, P. Laroche, and Z. Róka, eds. (IEEE, 2014), pp. 747–752.

2015 (8)

D. Barchiesi and T. Grosges, “Inverse problem method: a complementary way for the design and the characterization of nanostructures,” AASCIT Commun. 2, 296–300 (2015).

S. Kessentini and D. Barchiesi, “Particle swarm optimization with adaptive inertia weight,” Int. J. Mach. Learn. Comput. 5, 368–373 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Control of the applicability of the dipole approximation for gold nanoparticles,” Adv. Studies Biol. 7, 403–412 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Short note on the dipole approximation for electric field enhancement by small metallic nanoparticles,” J. Opt. 17, 114003 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Errata: fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophoton. 8, 089996 (2015).
[Crossref]

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

S. Babar and J. H. Weaver, “Optical constants of Cu, Ag, and Au revisited,” Appl. Opt. 54, 477–481 (2015).
[Crossref]

D. Barchiesi, “The Lycurgus cup: inverse problem using photographs for characterization of matter,” J. Opt. Soc. Am. A 32, 1544–1555 (2015).
[Crossref]

2014 (2)

H. N. Verma, P. Singh, and R. M. Chavan, “Gold nanoparticle: synthesis and characterization,” Veterinary World 7, 72–77 (2014).
[Crossref]

J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
[Crossref]

2013 (2)

2012 (3)

2011 (4)

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520, 501–509 (2011).
[Crossref]

S. Kessentini, D. Barchiesi, T. Grosges, and M. Lamy de la Chapelle, “Selective and collaborative optimization methods for plasmonics: a comparison,” PIERS Online 7, 291–295 (2011).

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

V. V. Datsyuk and O. M. Tovkach, “Optical properties of a metal nanosphere with spatially dispersive permittivity,” J. Opt. Soc. Am. B 28, 1224–1230 (2011).
[Crossref]

2009 (3)

2008 (2)

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
[Crossref]

2007 (1)

W. Haiss, N. T. K. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-VIS spectra,” Anal. Chem. 79, 4215–4221 (2007).
[Crossref]

2006 (4)

Y. Mori, M. Furukawa, T. Hayashi, and K. Nakamura, “Size distribution of gold nanoparticles used by small angle x-ray scattering,” Part. Sci. Technol. 24, 97–103 (2006).
[Crossref]

N. Harris, M. J. Ford, and M. B. Cortie, “Optimization of plasmonic heating by gold nanospheres and nanoshells,” J. Phys. Chem. B 110, 10701–10707 (2006).
[Crossref]

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

P. Stoller, V. Jacobsen, and V. Sandoghdar, “Measurement of the complex dielectric constant of a single gold nanoparticle,” Opt. Lett. 31, 2474–2476 (2006).
[Crossref]

2005 (3)

D. Macias and D. Barchiesi, “Identification of unknown experimental parameters from noisy apertureless scanning near-field optical microscope data with an evolutionary procedure,” Opt. Lett. 30, 2557–2559 (2005).
[Crossref]

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[Crossref]

J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
[Crossref]

2004 (1)

2003 (1)

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

2002 (2)

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

L. Kirkup, “A guide to gum,” Eur. J. Phys. 23, 483–487 (2002).
[Crossref]

2001 (1)

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
[Crossref]

2000 (1)

S. Link and M. A. El-Sayed, “Shape and size dependence of radiative, non-radiative and photothermal properties of gold nanocrystals,” Int. Rev. Phys. Chem. 19, 409–453 (2000).
[Crossref]

1999 (4)

T. Hayakawa, S. T. Selvan, and M. Nogami, “Field enhancement effect of small Ag particles on the fluorescence from Eu3+-doped SiO2 glass,” Appl. Phys. Lett. 74, 1513–1515 (1999).
[Crossref]

T. Pagnot, D. Barchiesi, and G. Tribillon, “Energy transfer from fluorescent thin films to metals in near-field optical microscopy: comparison between time-resolved and intensity measurements,” Appl. Phys. Lett. 75, 4207–4209 (1999).
[Crossref]

G. Parent, D. Van Labeke, and D. Barchiesi, “Surface imaging in near-field optical microscopy by using the fluorescence decay rate: a theoretical study,” J. Microsc. 194, 281–290 (1999).
[Crossref]

G. Parent, D. Van Labeke, and D. Barchiesi, “Fluorescence lifetime of a molecule near a corrugated interface: application to near-field microscopy,” J. Opt. Soc. Am. A 16, 896–908 (1999).
[Crossref]

1998 (1)

1997 (2)

1995 (1)

M. Futamata, “Surface-plasmon-polariton-enhanced Raman scattering from self-assembled monolayers of p-nitrothiophenol and p-aminothiophenol on silver,” J. Phys. Chem. 99, 11901–11908 (1995).
[Crossref]

1979 (1)

1976 (1)

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

1967 (1)

H. W. Lilliefors, “On the Kolmogorov-Smirnov test for normality with mean and variance unknown,” J. Am. Stat. Assoc. 62, 399–402 (1967).
[Crossref]

1965 (1)

S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality (complete samples),” Biometrika 52, 591–611 (1965).
[Crossref]

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[Crossref]

1954 (1)

T. W. Anderson and D. A. Darling, “A test of goodness of fit,” J. Am. Stat. Assoc. 49, 765–769 (1954).
[Crossref]

1944 (1)

K. Levenberg, “A method for the solution of certain problems in least squares,” Quart. Appl. Math. 2, 164–168 (1944).
[Crossref]

1933 (1)

A. Kolmogoroff, “Sulla determinazione empirica di una legge di distribuzione,” G. Ist. Ital. Attuari 4, 83–91 (1933).

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. 33025, 377–445 (1908).
[Crossref]

Adam, P.-M.

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
[Crossref]

Anderson, T. W.

T. W. Anderson and D. A. Darling, “A test of goodness of fit,” J. Am. Stat. Assoc. 49, 765–769 (1954).
[Crossref]

Arenas-Alatorre, J.

Aubard, J.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Aussenegg, F. R.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Aveyard, J.

W. Haiss, N. T. K. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-VIS spectra,” Anal. Chem. 79, 4215–4221 (2007).
[Crossref]

Babar, S.

Baffou, C.

Bakr, O. M.

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

Barchiesi, D.

S. Kessentini and D. Barchiesi, “Particle swarm optimization with adaptive inertia weight,” Int. J. Mach. Learn. Comput. 5, 368–373 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Control of the applicability of the dipole approximation for gold nanoparticles,” Adv. Studies Biol. 7, 403–412 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Short note on the dipole approximation for electric field enhancement by small metallic nanoparticles,” J. Opt. 17, 114003 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Inverse problem method: a complementary way for the design and the characterization of nanostructures,” AASCIT Commun. 2, 296–300 (2015).

D. Barchiesi and T. Grosges, “Errata: fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophoton. 8, 089996 (2015).
[Crossref]

D. Barchiesi, “The Lycurgus cup: inverse problem using photographs for characterization of matter,” J. Opt. Soc. Am. A 32, 1544–1555 (2015).
[Crossref]

J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
[Crossref]

D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36, 173–209 (2013).

D. Barchiesi, S. Kessentini, N. Guillot, M. Lamy de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21, 2245–2262 (2013).
[Crossref]

D. Barchiesi, “Numerical retrieval of thin aluminium layer properties from SPR experimental data,” Opt. Express 20, 9064–9078 (2012).
[Crossref]

S. Kessentini, D. Barchiesi, T. Grosges, and M. Lamy de la Chapelle, “Selective and collaborative optimization methods for plasmonics: a comparison,” PIERS Online 7, 291–295 (2011).

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
[Crossref]

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[Crossref]

D. Macias and D. Barchiesi, “Identification of unknown experimental parameters from noisy apertureless scanning near-field optical microscope data with an evolutionary procedure,” Opt. Lett. 30, 2557–2559 (2005).
[Crossref]

D. Macías, A. Vial, and D. Barchiesi, “Application of evolution strategies for the solution of an inverse problem in near-field optics,” J. Opt. Soc. Am. A 21, 1465–1471 (2004).
[Crossref]

T. Pagnot, D. Barchiesi, and G. Tribillon, “Energy transfer from fluorescent thin films to metals in near-field optical microscopy: comparison between time-resolved and intensity measurements,” Appl. Phys. Lett. 75, 4207–4209 (1999).
[Crossref]

G. Parent, D. Van Labeke, and D. Barchiesi, “Surface imaging in near-field optical microscopy by using the fluorescence decay rate: a theoretical study,” J. Microsc. 194, 281–290 (1999).
[Crossref]

G. Parent, D. Van Labeke, and D. Barchiesi, “Fluorescence lifetime of a molecule near a corrugated interface: application to near-field microscopy,” J. Opt. Soc. Am. A 16, 896–908 (1999).
[Crossref]

T. Pagnot, D. Barchiesi, D. van Labeke, and C. Pieralli, “Use of SNOM architecture to study fluorescence and energy transfer near a metal,” Opt. Lett. 22, 120–122 (1997).
[Crossref]

D. Barchiesi, “Handling uncertainties of models inputs in inverse problem: the U-discrete PSO approach,” in International Conference on Control, Decision and Information Technologies (CoDIT), I. Kacem, P. Laroche, and Z. Róka, eds. (IEEE, 2014), pp. 747–752.

D. Barchiesi, “Surface Plasmon Resonance Biosensors: Model and Optimization,” in Nanoantenna: Plasmon-Enhanced Spectroscopies for Biotechnological Applications, M. L. De la Chapelle and A. Pucci, eds. (Pan Stanford, 2013), Chap. 11, pp. 333–357.

D. Barchiesi, Numerical Optimization of Plasmonic Biosensors (INTECH Open Access, 2011), Chap. 5, pp. 105–126.

S. Kessentini and D. Barchiesi, Nanostructured Biosensors: Influence of Adhesion Layer, Roughness and Size on the LSPR: A Parametric Study (INTECH Open Access, 2013), Chap. 12, pp. 311–330.

D. Barchiesi, “Adaptive non-uniform, hyper-elitist evolutionary method for the optimization of plasmonic biosensors,” in CIE 2009 International Conference Computers & Industrial Engineering (2009), pp. 542–547.

Bateman, D.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave Version 4.2.0 Manual: A High-Level Interactive Language for Numerical Computations (2016).

Bienert, R.

R. Bienert, F. Emmerling, and A. F. Thünemann, “The size distribution of ‘gold standard’ nanoparticles,” Anal. Bioanal. Chem. 395, 1651–1660 (2009).
[Crossref]

Bijeon, J.-L.

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
[Crossref]

Billot, L.

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Boreman, G. D.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Borovkov, A. A.

A. A. Borovkov, Mathematical Statistics (Gordon and Breach Science, 1998).

Box, G. E. P.

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).

Carney, R. P.

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

Chavan, R. M.

H. N. Verma, P. Singh, and R. M. Chavan, “Gold nanoparticle: synthesis and characterization,” Veterinary World 7, 72–77 (2014).
[Crossref]

Cheang-Wong, J. C.

Chew, H.

P. J. McNumy, S. D. Druger, M. Kerker, and H. Chew, “Fluorescent scattering by anisotropic molecules embedded in small particles,” Appl. Opt. 18, 1484–1488 (1979).
[Crossref]

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Cortie, M. B.

N. Harris, M. J. Ford, and M. B. Cortie, “Optimization of plasmonic heating by gold nanospheres and nanoshells,” J. Phys. Chem. B 110, 10701–10707 (2006).
[Crossref]

Crespo-Sosa, A.

Darling, D. A.

T. W. Anderson and D. A. Darling, “A test of goodness of fit,” J. Am. Stat. Assoc. 49, 765–769 (1954).
[Crossref]

Datsyuk, V. V.

de la Chapelle, M. L.

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
[Crossref]

Djurišic, A. B.

Druger, S. D.

Eaton, J. W.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave Version 4.2.0 Manual: A High-Level Interactive Language for Numerical Computations (2016).

Elazar, J. M.

El-Sayed, M. A.

S. Link and M. A. El-Sayed, “Shape and size dependence of radiative, non-radiative and photothermal properties of gold nanocrystals,” Int. Rev. Phys. Chem. 19, 409–453 (2000).
[Crossref]

Emmerling, F.

R. Bienert, F. Emmerling, and A. F. Thünemann, “The size distribution of ‘gold standard’ nanoparticles,” Anal. Bioanal. Chem. 395, 1651–1660 (2009).
[Crossref]

Félidj, N.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Fernig, D. G.

W. Haiss, N. T. K. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-VIS spectra,” Anal. Chem. 79, 4215–4221 (2007).
[Crossref]

Ford, M. J.

N. Harris, M. J. Ford, and M. B. Cortie, “Optimization of plasmonic heating by gold nanospheres and nanoshells,” J. Phys. Chem. B 110, 10701–10707 (2006).
[Crossref]

Furukawa, M.

Y. Mori, M. Furukawa, T. Hayashi, and K. Nakamura, “Size distribution of gold nanoparticles used by small angle x-ray scattering,” Part. Sci. Technol. 24, 97–103 (2006).
[Crossref]

Futamata, M.

M. Futamata, “Surface-plasmon-polariton-enhanced Raman scattering from self-assembled monolayers of p-nitrothiophenol and p-aminothiophenol on silver,” J. Phys. Chem. 99, 11901–11908 (1995).
[Crossref]

Gao, L.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520, 501–509 (2011).
[Crossref]

Grand, J.

J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
[Crossref]

Gréhan, G.

Grimault, A. S.

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

Grimault, A.-S.

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[Crossref]

Grosges, T.

D. Barchiesi and T. Grosges, “Errata: fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophoton. 8, 089996 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Short note on the dipole approximation for electric field enhancement by small metallic nanoparticles,” J. Opt. 17, 114003 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Control of the applicability of the dipole approximation for gold nanoparticles,” Adv. Studies Biol. 7, 403–412 (2015).
[Crossref]

D. Barchiesi and T. Grosges, “Inverse problem method: a complementary way for the design and the characterization of nanostructures,” AASCIT Commun. 2, 296–300 (2015).

D. Barchiesi, S. Kessentini, N. Guillot, M. Lamy de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21, 2245–2262 (2013).
[Crossref]

S. Kessentini, D. Barchiesi, T. Grosges, and M. Lamy de la Chapelle, “Selective and collaborative optimization methods for plasmonics: a comparison,” PIERS Online 7, 291–295 (2011).

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
[Crossref]

Guillot, N.

Haiss, W.

W. Haiss, N. T. K. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-VIS spectra,” Anal. Chem. 79, 4215–4221 (2007).
[Crossref]

Harris, N.

N. Harris, M. J. Ford, and M. B. Cortie, “Optimization of plasmonic heating by gold nanospheres and nanoshells,” J. Phys. Chem. B 110, 10701–10707 (2006).
[Crossref]

Hauberg, S.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave Version 4.2.0 Manual: A High-Level Interactive Language for Numerical Computations (2016).

Hayakawa, T.

T. Hayakawa, S. T. Selvan, and M. Nogami, “Field enhancement effect of small Ag particles on the fluorescence from Eu3+-doped SiO2 glass,” Appl. Phys. Lett. 74, 1513–1515 (1999).
[Crossref]

Hayashi, T.

Y. Mori, M. Furukawa, T. Hayashi, and K. Nakamura, “Size distribution of gold nanoparticles used by small angle x-ray scattering,” Part. Sci. Technol. 24, 97–103 (2006).
[Crossref]

Hohenau, A.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Hunter, J. S.

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).

Hunter, W. G.

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).

Iotti, S.

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

Jacobsen, V.

Jayanti, S. V.

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

Jin, R.

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Johnson, T. W.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Kambe, H.

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
[Crossref]

Kellermann, G.

Kerker, M.

P. J. McNumy, S. D. Druger, M. Kerker, and H. Chew, “Fluorescent scattering by anisotropic molecules embedded in small particles,” Appl. Opt. 18, 1484–1488 (1979).
[Crossref]

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

Kessentini, S.

S. Kessentini and D. Barchiesi, “Particle swarm optimization with adaptive inertia weight,” Int. J. Mach. Learn. Comput. 5, 368–373 (2015).
[Crossref]

D. Barchiesi, S. Kessentini, N. Guillot, M. Lamy de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21, 2245–2262 (2013).
[Crossref]

S. Kessentini, D. Barchiesi, T. Grosges, and M. Lamy de la Chapelle, “Selective and collaborative optimization methods for plasmonics: a comparison,” PIERS Online 7, 291–295 (2011).

S. Kessentini and D. Barchiesi, Nanostructured Biosensors: Influence of Adhesion Layer, Roughness and Size on the LSPR: A Parametric Study (INTECH Open Access, 2013), Chap. 12, pp. 311–330.

Khurgin, J. B.

Kim, J. Y.

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

Kirkup, L.

L. Kirkup, “A guide to gum,” Eur. J. Phys. 23, 483–487 (2002).
[Crossref]

Kolmogoroff, A.

A. Kolmogoroff, “Sulla determinazione empirica di una legge di distribuzione,” G. Ist. Ital. Attuari 4, 83–91 (1933).

Kremer, E.

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

Krenn, J. R.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Kress, S. J. P.

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

Kreuzer, M.

Kulzer, F.

Kuyatt, C. E.

B. N. Taylor and C. E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results (National Institute of Standards and Technology, 1994) (supersedes NIST Technical Note 1297, January 1993).

Lamprecht, B.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Lamy de la Chapelle, M.

D. Barchiesi, S. Kessentini, N. Guillot, M. Lamy de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21, 2245–2262 (2013).
[Crossref]

S. Kessentini, D. Barchiesi, T. Grosges, and M. Lamy de la Chapelle, “Selective and collaborative optimization methods for plasmonics: a comparison,” PIERS Online 7, 291–295 (2011).

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[Crossref]

Leitner, A.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Lemarchand, F.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520, 501–509 (2011).
[Crossref]

Lequime, M.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520, 501–509 (2011).
[Crossref]

Levenberg, K.

K. Levenberg, “A method for the solution of certain problems in least squares,” Quart. Appl. Math. 2, 164–168 (1944).
[Crossref]

Lévi, G.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Lilliefors, H. W.

H. W. Lilliefors, “On the Kolmogorov-Smirnov test for normality with mean and variance unknown,” J. Am. Stat. Assoc. 62, 399–402 (1967).
[Crossref]

Link, S.

S. Link and M. A. El-Sayed, “Shape and size dependence of radiative, non-radiative and photothermal properties of gold nanocrystals,” Int. Rev. Phys. Chem. 19, 409–453 (2000).
[Crossref]

Macias, D.

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[Crossref]

D. Macias and D. Barchiesi, “Identification of unknown experimental parameters from noisy apertureless scanning near-field optical microscope data with an evolutionary procedure,” Opt. Lett. 30, 2557–2559 (2005).
[Crossref]

Macías, D.

Macready, W.

D. H. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1, 67–82 (1997).
[Crossref]

Mai, V. P.

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

Majewski, M. L.

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[Crossref]

McNulty, P. J.

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

McNumy, P. J.

McPeak, K. M.

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

Mehenni, H.

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

Meyer, S.

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. 33025, 377–445 (1908).
[Crossref]

Mori, Y.

Y. Mori, M. Furukawa, T. Hayashi, and K. Nakamura, “Size distribution of gold nanoparticles used by small angle x-ray scattering,” Part. Sci. Technol. 24, 97–103 (2006).
[Crossref]

Na, O. P.

Nakamura, H.

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
[Crossref]

Nakamura, K.

Y. Mori, M. Furukawa, T. Hayashi, and K. Nakamura, “Size distribution of gold nanoparticles used by small angle x-ray scattering,” Part. Sci. Technol. 24, 97–103 (2006).
[Crossref]

Nogami, M.

T. Hayakawa, S. T. Selvan, and M. Nogami, “Field enhancement effect of small Ag particles on the fluorescence from Eu3+-doped SiO2 glass,” Appl. Phys. Lett. 74, 1513–1515 (1999).
[Crossref]

Norris, D. J.

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

Oh, S.-H.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Oliver, A.

Olmon, R. L.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Otto, A.

D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36, 173–209 (2013).

Pagnot, T.

T. Pagnot, D. Barchiesi, and G. Tribillon, “Energy transfer from fluorescent thin films to metals in near-field optical microscopy: comparison between time-resolved and intensity measurements,” Appl. Phys. Lett. 75, 4207–4209 (1999).
[Crossref]

T. Pagnot, D. Barchiesi, D. van Labeke, and C. Pieralli, “Use of SNOM architecture to study fluorescence and energy transfer near a metal,” Opt. Lett. 22, 120–122 (1997).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants (Academic, 1985).

Parent, G.

G. Parent, D. Van Labeke, and D. Barchiesi, “Fluorescence lifetime of a molecule near a corrugated interface: application to near-field microscopy,” J. Opt. Soc. Am. A 16, 896–908 (1999).
[Crossref]

G. Parent, D. Van Labeke, and D. Barchiesi, “Surface imaging in near-field optical microscopy by using the fluorescence decay rate: a theoretical study,” J. Microsc. 194, 281–290 (1999).
[Crossref]

Pieralli, C.

Qian, H.

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

Quidant, R.

Rakic, A. D.

Raschke, M. B.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Rodríguez-Fernández, L.

Rodríguez-Iglesias, V.

Rossinelli, A.

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

Royer, P.

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
[Crossref]

Saiki, T.

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
[Crossref]

Salerno, M.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Salvi, J.

J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
[Crossref]

Sandoghdar, V.

Sato, T.

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
[Crossref]

Sawada, K.

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
[Crossref]

Schider, G.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

Selvan, S. T.

T. Hayakawa, S. T. Selvan, and M. Nogami, “Field enhancement effect of small Ag particles on the fluorescence from Eu3+-doped SiO2 glass,” Appl. Phys. Lett. 74, 1513–1515 (1999).
[Crossref]

Shapiro, S. S.

S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality (complete samples),” Biometrika 52, 591–611 (1965).
[Crossref]

Shelton, D.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Silva-Pereyra, H. G.

Singh, P.

H. N. Verma, P. Singh, and R. M. Chavan, “Gold nanoparticle: synthesis and characterization,” Veterinary World 7, 72–77 (2014).
[Crossref]

Slovick, B.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Stellacci, F.

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

Stoller, P.

Sun, G.

Tarantola, A.

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation (Society for Industrial and Applied Mathematics, 2005).

Taylor, B. N.

B. N. Taylor and C. E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results (National Institute of Standards and Technology, 1994) (supersedes NIST Technical Note 1297, January 1993).

Thanh, N. T. K.

W. Haiss, N. T. K. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-VIS spectra,” Anal. Chem. 79, 4215–4221 (2007).
[Crossref]

Thünemann, A. F.

R. Bienert, F. Emmerling, and A. F. Thünemann, “The size distribution of ‘gold standard’ nanoparticles,” Anal. Bioanal. Chem. 395, 1651–1660 (2009).
[Crossref]

Toury, T.

Tovkach, O. M.

Tribillon, G.

T. Pagnot, D. Barchiesi, and G. Tribillon, “Energy transfer from fluorescent thin films to metals in near-field optical microscopy: comparison between time-resolved and intensity measurements,” Appl. Phys. Lett. 75, 4207–4209 (1999).
[Crossref]

Tsai, D. P.

Van Labeke, D.

Verma, H. N.

H. N. Verma, P. Singh, and R. M. Chavan, “Gold nanoparticle: synthesis and characterization,” Veterinary World 7, 72–77 (2014).
[Crossref]

Vial, A.

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
[Crossref]

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[Crossref]

D. Macías, A. Vial, and D. Barchiesi, “Application of evolution strategies for the solution of an inverse problem in near-field optics,” J. Opt. Soc. Am. A 21, 1465–1471 (2004).
[Crossref]

Weaver, J. H.

Wehbring, R.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave Version 4.2.0 Manual: A High-Level Interactive Language for Numerical Computations (2016).

Wilk, M. B.

S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality (complete samples),” Biometrika 52, 591–611 (1965).
[Crossref]

Wolpert, D. H.

D. H. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1, 67–82 (1997).
[Crossref]

AASCIT Commun. (1)

D. Barchiesi and T. Grosges, “Inverse problem method: a complementary way for the design and the characterization of nanostructures,” AASCIT Commun. 2, 296–300 (2015).

ACS Photon. (1)

K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015).
[Crossref]

Adv. Studies Biol. (1)

D. Barchiesi and T. Grosges, “Control of the applicability of the dipole approximation for gold nanoparticles,” Adv. Studies Biol. 7, 403–412 (2015).
[Crossref]

Anal. Bioanal. Chem. (1)

R. Bienert, F. Emmerling, and A. F. Thünemann, “The size distribution of ‘gold standard’ nanoparticles,” Anal. Bioanal. Chem. 395, 1651–1660 (2009).
[Crossref]

Anal. Chem. (1)

W. Haiss, N. T. K. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-VIS spectra,” Anal. Chem. 79, 4215–4221 (2007).
[Crossref]

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. 33025, 377–445 (1908).
[Crossref]

Appl. Opt. (4)

Appl. Phys. A (1)

J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
[Crossref]

Appl. Phys. Lett. (3)

T. Hayakawa, S. T. Selvan, and M. Nogami, “Field enhancement effect of small Ag particles on the fluorescence from Eu3+-doped SiO2 glass,” Appl. Phys. Lett. 74, 1513–1515 (1999).
[Crossref]

T. Pagnot, D. Barchiesi, and G. Tribillon, “Energy transfer from fluorescent thin films to metals in near-field optical microscopy: comparison between time-resolved and intensity measurements,” Appl. Phys. Lett. 75, 4207–4209 (1999).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. 82, 3095–3097 (2003).
[Crossref]

Biometrika (1)

S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality (complete samples),” Biometrika 52, 591–611 (1965).
[Crossref]

Chem. Phys. Lett. (1)

L. Billot, M. L. de la Chapelle, A. S. Grimault, A. Vial, D. Barchiesi, J.-L. Bijeon, P.-M. Adam, and P. Royer, “Surface enhanced Raman scattering on gold nanowire arrays: evidence of strong multipolar surface plasmon resonance enhancement,” Chem. Phys. Lett. 422, 303–307 (2006).
[Crossref]

Eur. J. Phys. (1)

L. Kirkup, “A guide to gum,” Eur. J. Phys. 23, 483–487 (2002).
[Crossref]

G. Ist. Ital. Attuari (1)

A. Kolmogoroff, “Sulla determinazione empirica di una legge di distribuzione,” G. Ist. Ital. Attuari 4, 83–91 (1933).

IEEE Trans. Evol. Comput. (1)

D. H. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1, 67–82 (1997).
[Crossref]

Int. J. Mach. Learn. Comput. (1)

S. Kessentini and D. Barchiesi, “Particle swarm optimization with adaptive inertia weight,” Int. J. Mach. Learn. Comput. 5, 368–373 (2015).
[Crossref]

Int. Rev. Phys. Chem. (1)

S. Link and M. A. El-Sayed, “Shape and size dependence of radiative, non-radiative and photothermal properties of gold nanocrystals,” Int. Rev. Phys. Chem. 19, 409–453 (2000).
[Crossref]

J. Am. Stat. Assoc. (2)

T. W. Anderson and D. A. Darling, “A test of goodness of fit,” J. Am. Stat. Assoc. 49, 765–769 (1954).
[Crossref]

H. W. Lilliefors, “On the Kolmogorov-Smirnov test for normality with mean and variance unknown,” J. Am. Stat. Assoc. 62, 399–402 (1967).
[Crossref]

J. Microsc. (3)

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
[Crossref]

G. Parent, D. Van Labeke, and D. Barchiesi, “Surface imaging in near-field optical microscopy by using the fluorescence decay rate: a theoretical study,” J. Microsc. 194, 281–290 (1999).
[Crossref]

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

J. Nanophoton. (1)

D. Barchiesi and T. Grosges, “Errata: fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophoton. 8, 089996 (2015).
[Crossref]

J. Opt. (1)

D. Barchiesi and T. Grosges, “Short note on the dipole approximation for electric field enhancement by small metallic nanoparticles,” J. Opt. 17, 114003 (2015).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

J. Phys. Chem. (1)

M. Futamata, “Surface-plasmon-polariton-enhanced Raman scattering from self-assembled monolayers of p-nitrothiophenol and p-aminothiophenol on silver,” J. Phys. Chem. 99, 11901–11908 (1995).
[Crossref]

J. Phys. Chem. B (1)

N. Harris, M. J. Ford, and M. B. Cortie, “Optimization of plasmonic heating by gold nanospheres and nanoshells,” J. Phys. Chem. B 110, 10701–10707 (2006).
[Crossref]

J. Soc. Ind. Appl. Math. (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[Crossref]

Nat. Commun. (1)

R. P. Carney, J. Y. Kim, H. Qian, R. Jin, H. Mehenni, F. Stellacci, and O. M. Bakr, “Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation,” Nat. Commun. 2, 335 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

Part. Sci. Technol. (1)

Y. Mori, M. Furukawa, T. Hayashi, and K. Nakamura, “Size distribution of gold nanoparticles used by small angle x-ray scattering,” Part. Sci. Technol. 24, 97–103 (2006).
[Crossref]

Phys. Rev. A (1)

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

Phys. Rev. B (5)

J. Grand, M. L. de la Chapelle, J.-L. Bijeon, P.-M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72, 033407 (2005).
[Crossref]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering,” Phys. Rev. B 65, 075419 (2002).
[Crossref]

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

PIERS Online (1)

S. Kessentini, D. Barchiesi, T. Grosges, and M. Lamy de la Chapelle, “Selective and collaborative optimization methods for plasmonics: a comparison,” PIERS Online 7, 291–295 (2011).

Quart. Appl. Math. (1)

K. Levenberg, “A method for the solution of certain problems in least squares,” Quart. Appl. Math. 2, 164–168 (1944).
[Crossref]

Riv. Nuovo Cimento (1)

D. Barchiesi and A. Otto, “Excitations of surface plasmon polaritons by attenuated total reflection, revisited,” Riv. Nuovo Cimento 36, 173–209 (2013).

Thin Solid Films (1)

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films 520, 501–509 (2011).
[Crossref]

Veterinary World (1)

H. N. Verma, P. Singh, and R. M. Chavan, “Gold nanoparticle: synthesis and characterization,” Veterinary World 7, 72–77 (2014).
[Crossref]

Other (17)

http://refractiveindex.info , 2016.

E. D. Palik, Handbook of Optical Constants (Academic, 1985).

D. Barchiesi, “Adaptive non-uniform, hyper-elitist evolutionary method for the optimization of plasmonic biosensors,” in CIE 2009 International Conference Computers & Industrial Engineering (2009), pp. 542–547.

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation (Society for Industrial and Applied Mathematics, 2005).

D. Barchiesi, “Surface Plasmon Resonance Biosensors: Model and Optimization,” in Nanoantenna: Plasmon-Enhanced Spectroscopies for Biotechnological Applications, M. L. De la Chapelle and A. Pucci, eds. (Pan Stanford, 2013), Chap. 11, pp. 333–357.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

D. Barchiesi, Numerical Optimization of Plasmonic Biosensors (INTECH Open Access, 2011), Chap. 5, pp. 105–126.

S. Kotz and N. L. Johnson, eds., Breakthroughs in Statistics: Methodology and Distribution (Springer, 1992).

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).

S. Kessentini and D. Barchiesi, Nanostructured Biosensors: Influence of Adhesion Layer, Roughness and Size on the LSPR: A Parametric Study (INTECH Open Access, 2013), Chap. 12, pp. 311–330.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave Version 4.2.0 Manual: A High-Level Interactive Language for Numerical Computations (2016).

A. A. Borovkov, Mathematical Statistics (Gordon and Breach Science, 1998).

Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1), “Evaluation of measurement data—Guide to the expression of uncertainty in measurement,” 1st ed., (GUM 1995 with minor corrections) (2008).

Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1), “Evaluation of measurement data—Supplement 1 to the ‘Guide to the expression of uncertainty in measurement’—Propagation of distributions using a Monte Carlo method,” 1st ed., (2008).

Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1), “Evaluation of measurement data—Supplement 2 to the ‘Guide to the expression of uncertainty in measurement’—Extension to any number of output quantities,” 1st ed., (2011).

B. N. Taylor and C. E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results (National Institute of Standards and Technology, 1994) (supersedes NIST Technical Note 1297, January 1993).

D. Barchiesi, “Handling uncertainties of models inputs in inverse problem: the U-discrete PSO approach,” in International Conference on Control, Decision and Information Technologies (CoDIT), I. Kacem, P. Laroche, and Z. Róka, eds. (IEEE, 2014), pp. 747–752.

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Figures (11)

Fig. 1.
Fig. 1.

Real part of the relative permittivity of gold from various references as a function of the photon energy hν=ω. Drude–Lorentz fitting of data from [46] (dashed line [52] and solid line [53]); experimental data from [4651].

Fig. 2.
Fig. 2.

Imaginary part of the relative permittivity of gold from various references as a function of the photon energy hν=ω. Drude–Lorentz fitting of data from [46] (dashed line [52] and solid line [53]); experimental data from [4651].

Fig. 3.
Fig. 3.

Minimum, maximum, and mean value of the real (black) and imaginary (gray) parts of the relative permittivity used for computing the uncertainty as a function of the wavelength λ0.

Fig. 4.
Fig. 4.

Contribution of each term in the sum in Eq. (20) to the combined uncertainty calculated from the dipole approximation. TR2 [Eq. (21)], TRe2 [Eq. (22)], TIm2 [Eq. (23)], and Tρ [Eq. (24)] are the respective contributions of the uncertainties of the radius R=25  nm, of the real and the imaginary parts of the relative permittivity of gold, and of Pearson’s correlation coefficient ρ(R(εr),I(εr)).

Fig. 5.
Fig. 5.

Scattering efficiency calculated with the dipole approximation [Eq. (16); black solid line] and with the full Mie theory [Eq. (12); gray solid line] for a particle radius R=25  nm. Uncertainty bars are shown [Qscad(μ(εr))u(Qscad);Qscad(μ(εr))+u(Qscad)] [Eqs. (16) and (20)].

Fig. 6.
Fig. 6.

Minimum and maximum of the relative errors (in percent) e(λr,λrd) (black lines) and e(maxλ0(Qsca),maxλ0(Qscad)) (gray lines) as functions of the nanoparticle radius R. All experimental values of the relative permittivity of gold cited in Section 3.B are used.

Fig. 7.
Fig. 7.

Quantile-to-quantile plot of values of the maximum of the scattering efficiencies maxλ0(Qsca) (black) and maxλ0(Qscad) (gray).

Fig. 8.
Fig. 8.

Quantile-to-quantile plot of the resonant wavelengths λr (black) and λrd (gray).

Fig. 9.
Fig. 9.

Scatter plot of a realization of the statistical method: resonance of the scattering efficiencies maxλ0(Qsca) (black) and maxλ0(Qscad) (gray) as a function of λr, the wavelength at which resonance occurs. Deterministic calculation for R[22.5;27.5]  nm and the mean value of εr (thick segments).

Fig. 10.
Fig. 10.

Correlation matrix of the input parameters, variable, and outputs: the mean values of the real and imaginary parts of the relative permittivity of gold (εr), the radius R, the values of the scattering efficiency maximum maxλ0(Qsca), and the resonant wavelength λr, calculated from the full Mie theory. All the output data O of size 80,400 are used.

Fig. 11.
Fig. 11.

Scatter plot of the sorted results of the propagation of uncertainties. Scattering efficiency calculated from the full Mie theory (gray lines) and from the dipole approximation (black lines), using the mean value of the relative permittivities of gold for each wavelength. Uncertainties are calculated for μ(R)=19, 21, 23, 25, 27, and 29 nm with the method of propagation of uncertainties.

Tables (10)

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Table 1. Values for maxλ0(Qsca) (Full Mie Theory) and maxλ0(Qscad) (Dipole Approximation), λr (Full Mie Theory) and λrd (Dipole Approximation): Mean Value μ, Standard Deviation σ, and Coverage Intervals CI95%c, for a Coverage Factor p=95%a

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Table 2. Values for maxλ0(Qsca) (Full Mie Theory) and maxλ0(Qscad) (Dipole Approximation): Mean Value μ, Standard Deviation σ, Results of Tests [Lilliefors (pSK), Anderson–Darling (pAD), Shapiro–Wilk (pSW), Pearson (pχ2)], Coverage Factors for the Sample zs and for the Mean Value zm, and Coverage Intervals of the Sample CI and of the Mean Value CIμa

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Table 3. Values for λr (Full Mie Theory) and λrd (Dipole Approximation): Mean Value μ, Standard Deviation σ, Results of Tests [Lilliefors (pSK), Anderson–Darling (pAD), Shapiro–Wilk (pSW), Pearson (pχ2)], Coverage Factors for the Sample zs and for the Mean Value zm, and Coverage Intervals of the Sample CI and of the Mean Value CIμa

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Algorithm 1 Propagation of uncertainties algorithm. The number of inputs of the model is N [N=3 in our case: (R,R(εr),I(εr))]. All vectors are of dimension M (M=400). Mn is the numerical model, p is the coverage probability, μ is the average (or mean value), and σ is the standard deviation. ur(o) is the target accuracy for the output data.

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Algorithm 2 Propagation of uncertainties function Mn is the numerical model, p is the coverage probability, μ is the average (or mean value), and σ is the standard deviation. ur(o) is the target accuracy for the output data.

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Algorithm 3 Coverage interval · is the integer part (see Section 7.7 of Ref. [2]).

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Table 4. Summary of the Notations, Quantities, and Uncertainties for Models (Sections 2 and 3)

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Table 5. Summary of the General Notations for Statistics, Propagation of Uncertainties, Optimization, and Inverse Problems (Sections 2 and 3)

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Table 6. Summary of the Notations and Quantities for Coverage Intervals (Sections 2 and 3)

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Table 7. Summary of the Notations and Quantities for the Scattering of Light by Nanoparticles

Equations (36)

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u2(o)=i=1N(MaIi)2u2(Ii)+2i=1N1j=i+1N[ρ(Ii,Ij)(MaIi)(MaIj)u(Ii)u(Ij)sensitivity coefficientsciandcj],
ρ(Ii,Ij)=(Iiμ(Ii))(Ijμ(Ij))((Iiμ(Ii))2)1/2((Ijμ(Ij))2)1/2,
sy=max({sμ,su(O),sylow,syhigh})ur(o).
CIp%=[μzsσ;μ+zsσ],
zs=CDFN(0,1)1(1p2).
CIp%μ=[μzmσM;μ+zmσM].
zm=CDFt1(1p2).
νeff=u4(o)(ci4ui4(Ii)νi).
er(o1,o2)=(1o2o1).
oO>tO×max(o),
T(1tI)oIT(1+tI).
Qsca=2x2n=1+(2n+1)(|an|2+|bn|2).
an=m2jn(mx)[xjn(x)]jn(x)[mxjn(mx)]m2jn(mx)[xhn(1)(x)]hn(1)(x)[mxjn(mx)],
bn=jn(mx)[xjn(x)]jn(x)[mxjn(mx)]jn(mx)[xhn(1)(x)]hn(1)(x)[mxjn(mx)],
Qsca=Qscad+165[|εr1|2(|εr|24)|εr+2|4]x6323[I(εr)|εr1|2|εr+2|4]x7,
Qscad=83|εr1|2|εr+2|2x4,
u(R)=0.1R  or  ur(R)=10%,
u(R(εr(λ0)))=max(R(εr(λ0)))min(R(εr(λ0)))23,
u(I(εr(λ0)))=max(I(εr(λ0)))min(I(εr(λ0)))23.
ur2(Qscad)=u2(Qscad)(Qscad)2=TR2+TRe2+TIm2+Tρ,
QscadTR=(QscadR)u(R)=(323k|εr1|2|εr+2|2)x3u(R)=4u(R)R,
QscadTRe=(QscadR(εr))u(R(εr))=16x4u(R(εr))((R(εr)1)(R(εr)+2)(I(εr))|εr+2|4),
QscadTIm=(QscadI(εr))u(I(εr))=(16I(εr)(2R(εr)+1)|εr+2|4)x4u(I(εr)),
Tρ=2TReTImρ(R(εr),I(εr)).
sy=max({sμ,su(O),sylowsyhigh})ur(o),
νeff(maxλ0(Qscad))=u4(maxλ0(Qscad))TR2(λrd)219+TRe2(λrd)19+TIm2(λrd)19.
maxλ0Qsca=(0.1174±0.0051),
maxλ0Qscad=(0.0977±0.0040),
λr=(518.55±0.23)  nm,
λrd=(516.82±0.23)  nm,
R(εreff)=2(53C1)C1+5C2(4+3C1)C110C2,
I(εreff)=3(4C12+24C1320C1C225C22)(4C1+3C1210C2)2(16+5C2).
maxλ0(Qsca)=a0+a1R+a2R2+a3R3=0.1128+0.0487R+0.00839R2+0.000657R3.
R=13a3[(a2+21/3D1D2+D224D13)1/3+121/3(D2+D224D13)1/3],
D1=a223a1a3
D2=2a239a1a2a3+27a32(a0maxλ0(Qsca)).

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